151 research outputs found
A Nonlinear Multigrid Steady-State Solver for Microflow
We develop a nonlinear multigrid method to solve the steady state of
microflow, which is modeled by the high order moment system derived recently
for the steady-state Boltzmann equation with ES-BGK collision term. The solver
adopts a symmetric Gauss-Seidel iterative scheme nested by a local Newton
iteration on grid cell level as its smoother. Numerical examples show that the
solver is insensitive to the parameters in the implementation thus is quite
robust. It is demonstrated that expected efficiency improvement is achieved by
the proposed method in comparison with the direct time-stepping scheme
NRxx Simulation of Microflows with Shakhov Model
In this paper, we propose a method to simulate the microflows with Shakhov
model using the NRxx method developed in [4, 5, 6]. The equation under
consideration is the Boltzmann equation with force terms and the Shakhov model
is adopted to achieve the correct Prandtl number. As the focus of this paper,
we derive a uniform framework for different order moment systems on the wall
boundary conditions, which is a major difficulty in the moment methods.
Numerical examples for both steady and unsteady problems are presented to show
the convergence in the number of moments.Comment: 31 pages, 10 figure
Continuum Simulation of Fluid Flow and Heat Transfer in Gas Microsystems
The aim of the present work is to make use of the constitutive scaling method to produce a computational tool suitable for analysing microscale flows. Both incompressible and compressible numerical solvers featuring constitutive scaling models and a range of appropriate boundary conditions have been developed to this end. A detailed assessment of the implications of extending the constitutive scaling method to fully compressible flows has also been carried out
Continuum analysis of rarefaction effects on a thermally-induced gas flow
A Maxwell gas confined within a micro cavity with non-isothermal walls is
investigated in the slip and early transition regimes using the classical and
extended continuum theories. The vertical sides of the cavity are kept at the
uniform and environmental temperature T_0, while the upper and bottom ones are
linearly heated in opposite directions from the cold value T_0 to the hot
oneT_H. The gas flow is, therefore, induced only by the temperature gradient
created along the longitudinal walls. The problem is treated from a macroscopic
point of view by solving numerically the so-called regularized 13-moment
equations (R13) recently developed as an extension of Grad 13-moments theory to
the third order of the Knudsen number powers in the Chapman-Enskog expansion.
The gas macroscopic properties obtained by this method are compared with the
classical continuum theory results (NSF) using the first and second order of
velocity slip and temperature jump boundary conditions. The gas flow behavior
is studied as a function of the Knudsen number (Kn), nonlinear effects, for
different heating ratesT_0/T_H . The micro cavity aspect ratio effect is also
evaluated on the flow fields in this study.Comment: 18,9 figures, submitted to Mathematical Problems in Engineering
Journa
Kinetic Solvers with Adaptive Mesh in Phase Space
An Adaptive Mesh in Phase Space (AMPS) methodology has been developed for
solving multi-dimensional kinetic equations by the discrete velocity method. A
Cartesian mesh for both configuration (r) and velocity (v) spaces is produced
using a tree of trees data structure. The mesh in r-space is automatically
generated around embedded boundaries and dynamically adapted to local solution
properties. The mesh in v-space is created on-the-fly for each cell in r-space.
Mappings between neighboring v-space trees implemented for the advection
operator in configuration space. We have developed new algorithms for solving
the full Boltzmann and linear Boltzmann equations with AMPS. Several recent
innovations were used to calculate the discrete Boltzmann collision integral
with dynamically adaptive mesh in velocity space: importance sampling,
multi-point projection method, and the variance reduction method. We have
developed an efficient algorithm for calculating the linear Boltzmann collision
integral for elastic and inelastic collisions in a Lorentz gas. New AMPS
technique has been demonstrated for simulations of hypersonic rarefied gas
flows, ion and electron kinetics in weakly ionized plasma, radiation and light
particle transport through thin films, and electron streaming in
semiconductors. We have shown that AMPS allows minimizing the number of cells
in phase space to reduce computational cost and memory usage for solving
challenging kinetic problems
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